Wednesday, June 09, 2010

On Fecundity

A letter in the 3 June 2010 issue of Nature addresses "The role of mentorship in protégé performance". That sounds sort of interesting. I'd like to know ".. the extent to which protégés mimic their mentors' career choices and acquire their mentorship skills".

Those are two very different things, though. I can see how you could determine whether protégés follow the same career path as their advisers, but you need some assumptions to go from those data to interpretations about acquisition of mentorship skills (or lack thereof).

To address these issues, the authors (Malmgrenetal.) used a large database that has tracked mathematicians and their academic "genealogy" for centuries. Despite the massive database going back to 1637, the authors analyzed only the years 1900-1960 because these data were deemed "most reliable" and this range allows the tracking of a few generations.

More recent data would be interesting to consider as well, if possible, particularly to see if the culture of academic math departments has changed. Or perhaps nothing changes the culture of math departments; the authors concluded that, despite the occurrence of some world wars etc. in the 20th century, there were "no systematic historical changes" evident in the database.

The research was designed to evaluate whether protégés "acquire the mentorship skills of their mentors". This is done by studying mentorshipfecundity. I am not sure that fecundity necessarily relates to "mentorship skills" or "mentorship success", but that's how it was defined.

A brief aside: This may be a seminal paper, but I wish there were a different term that could be used than fecundity to represent the number of protégés a mentor trains. I also wish there were a better term than "protégé", although I know that technically the word is used appropriately in this paper. Advisee and mentee aren't great words either, but somehow they seem more professional to me. Or, if protégé must be used, can I be called a patron rather than a mentor?

Anyway, what we all want to know is:

Can you predict the fecundity of a mathematician?

Well, it's complicated, but you can write an equation! Also, you can make an analogy with parents (= mentors) and children (= protégés), such that a protégé's graduation date is their "birth date". I'm not sure why this new terminology was introduced, as the original concepts of mentor, protégé, and graduation date are not that complicated, but so it goes.

The results, which aren't actually explained in the paper, are "three significant correlations in mentorship fecundity", which I will condense into two:

1. Protégés of mentors with low fecundity (< 3 protégés) had more protégés than "expected".

2. The protégés of early-career mentors are themselves more fecund than "expected" and are more fecund than protégés who are advised by these same mentors later in their careers; i.e., fecundity might be influenced by the adviser's career stage.

The first interpretation did not surprise me, although one has to be clear about what the "expected" fecundity of protégés is before deciding if the result is greater or less than expected. The second one is more surprising, but whether it has any meaning depends, of course, on the methods and assumptions of the study.

It's a rather strange study and we can pick away at it, but is there anything to be learned from it about the influence of mentors on the later careers of their mentees? I doubt it, although I think the motivating question of the study is an interesting one, and perhaps impossible to study in a meaningful and quantitative way. To be relevant to modern mentorship, such a study would also have to track career paths that veer from math to engineering, or to any of various other interconnected disciplines.

And, because being a successful mentor doesn't have to mean that we clone ourselves and produce academic children who mimic our careers, perhaps there would need to be a different way of measuring the quality and success of mentorship than simply counting up the numbers of academic children and grandchildren and great-grandchildren.

24 comments:

Trabor
said...

It's an interesting idea for a study, but hard to pull off. I think the (undeniable?) historical events and their effects on mentoring since 1960 would make this time period more interesting and relevant to most of us. In 1960, I suspect I would have been mentored straight into a nice secretarial job, and straight to the stake in 1637.

The 2nd conclusion doesn't actually surprise me - I've noticed that many of my fellow junior faculty were early students (pre-tenure) for their PhD advisor. I don't know if it's the academically-minded self select for the new/challenging lab situation or if going through that situation where you have a more involved advisor and see what starting a faculty job is like better prepares you. Yes, these are broad generalizations - just something I've noticed.

I work at a Big Research University as an administrator--lots and lots of editing and writing, in particular. I spend much of my time removing "reproductive" words out of research profiles and bios like vigorous, virile, fruitful, prolific, potent, probing, stimulating, generative, thrust, stroke, and, of course fecund. Some of them are fine by themselves, but used all together in a pile in a short document, one can't help but wonder weird and creepy relationship some researchers bear to their work--and I suppose I can to add to this mix their advisees. And, oddly, it's more common to see these word choices for physics and math, where most researchers (though not all) around here are men...

Sorry to nitpick, but "seminal" is also in this class of words. I know it's a common word to use in reference to research, but most of its definition refer to seeds and semen in the OED. Maybe I'm just an oversensitive literary type, but it totes creeps me out.

Or maybe, if you're researching advisor "fecundity," "seminal" is the perfect word to use?

I strongly agree with your idea of not just looking at academic family trees. If you asked me who my mentor is, my first answer would not be my advisor, it would be another faculty member in the department.

I am a professor in the physical sciences where job prospects are few outside academia. My personal goal is to "mentor" students who will eventually go into diverse fields, some in academia and others who will adopt a totally different career. I am very proud of one of my mentees who has been a science writer. Does this protégé count against my fecondity?

As a math grad student, I think the more interesting question is why do mathematicians have so many vanity projects, such as the Erdos number calculator and the Math genealogy project (I would guess that this is the database mentioned in the post), at all? Or maybe all fields have them, and I just don't know the physics/biology/etc. equivalent.

Yeah, I wonder about the math-ego thing too. We've got one member of our dept. who does philosophy of math, so he's mostly a philosophy person, but he's inordinately proud of his math family tree, and he has the whole genealogy traced out. It just makes me gag.

@William: I don't think these are vanity projects but rather silliness projects.

A mathematician no longer completely plugged in to the research community decides that some piece of silliness is worth studying. Sure it's not exactly research at the frontiers of mathematics, but people find it amusing and interesting. Frankly, it's just as good a use of mathematics as the ridiculous examples folks put in calculus textbooks.

I think it's a positive aspect of the mathematical community that we appreciate endeavors like the Genealogy Project and Erdos Numbers. (This is excluding the few nutters who actually take these things seriously.) Who knows? Someone might eventually be able to extract some information out of the data.

Pardon me for a rather off topic comment, but the use of the word "seminal" in the post made me want to bring something up:

In the May issue of APS News there was a letter (http://www.aps.org/publications/apsnews/201005/letters.cfm) that suggested that we should move away from using the word "seminal" due to its "sexist" nature. I am not a native English speaker, so I has to look up the exact origin of the word before I understood why would anyone have such an idea. Still, I find it nothing short of absurd.

Most importantly I find it reassuring (that the world has not gone mad) that someone as sensitive to gender issues as the author of this blog, still finds "seminal" to be an acceptable word. I would also enjoy reading your thoughts on the subject (as long as they agreed with my opinion :)).

If it is any consolation, FSP, I recognized it as a joke (and thought it was hilarious) and I'm sure I'm not the only one. Furthermore, "seminal" is used to refer to seeds in plant biology, aka the offspring of the plant with some extra packaging from the maternal parent. I hate the phrase "seminal idea" or "seminal research," for the obvious reasons, but there are contexts in which the word "seminal" is legit, and shouldn't even creep out the most nitpicky of oversensitive literary types.

Regarding mathematician and vanity projects I don't think its quite that simple. Both the genealogy project and collaboration distance are essentially networks. This is likely to appeal to mathematicians anyway. Also your mathematical family is actually quite important. Although no one really cares who your distant ancestors were your immediate family and their standing has a huge impact on your success.

First, linguists believe that the seed meaning of seminal predates the semen meaning of seminal.

Second, if you have to look it up in a dictionary to realize that it could possibly be discriminatory, then it isn't.

Third, if you believe that removing seminal and stimulating from grant proposals in any way helps the status of women, I'm sad to say you've spent too much time in academia. Find a more worthy cause and spend time on that.

Second, I can't comment on the Erdos number calculator since I don't know what it is. But genealogy projects often have value to the history of science. These projects can show us how ideas, hypotheses, theorems, or other intellectual trends spread or change - we can often trace schools of thought by knowing who trained with whom.

Third, it's worth nothing that some of us are "fecund" DESPITE the mentoring skills of our advisors or professors, not because of them.

About Me

I am a full professor in a physical sciences field at a large research university. I am married and have a teenaged daughter.
I have the greatest job in the world, but this will not stop me from noting some of the more puzzling and stressful aspects of my career as a science professor.
E-mail (can't promise to reply): femalescienceprofessor@gmail.com